What is a "universal" disc rotor? One that is compatible with all types of brake pads?
Every brake manufacturer recommends only using their own rotors, so this is another case where the answer depends very much on who you ask.
In general, here is where rotor cross-compatibility can go wrong:
- Some inexpensive Shimano rotors have less hardening and are designated "resin only." They in fact wear very fast if a metallic or semi-metallic pad is used.
- Magura rotors are 2mm thick and more or less everyone else's are 1.8mm. Using a thicker rotor than a caliper is designed around, along with unworn pads, could get you into situations where you don't have enough air gap to play with even with the pistons all the way in. Such issues come up rarely in practice however.
- Different calipers can place the size and location of the pad contact patch on the rotor a little differently. It seems like in practice there is not a ton of variance, but there is some. Someone trying to design a universal rotor would be trying to make it big enough that the top of the pad on any caliper never overhangs the rotor, but the top of the rotor can never interfere with any caliper.
The main question with the idea of a universal rotor design is whether, given an on-spec location of the brake mounts, is there a magic number for the exact outside diameter needed in the last point. I don't know the answer to that. But for practical purposes, all of the above issues are rare, most rotors are designed to capture some aftermarket sales as generic repair parts, and it's all pretty cross-compatible as long as it's not resin-only or Magura.
Another subtle issue is the spacing of the vents. Ideally the pad will always contact the same amount of rotor, but if the pad size doesn't match the period of the vent pattern breaking can be uneven. This mostly seems to be an issue with fairly gentle braking.
Imagine a rotor with purely radial vents accounting for half the area swept by the pads. Now consider a pad the same width as two vents and the metal rib in between, or two ribs and one vent. The contact area changes periodically by a factor of two. As the contact force is constant, the braking force doesn't change by as much (under a simple picture with a constant coefficient of friction it wouldn't change at all). Both shape and dimensions are a little extreme as an example, but this was noticeable with a Shimano rotor I used with BB5-style brakes that have smaller pads than shimano use.